Oh, and just for clarity, I have measured the forces outside the fully enclosed cavity shown first above. The forces are identically zero for the fully enclosed cavity as has been proven mathematically time and again.

<< I have measured the forces outside the fully enclosed cavity shown first above. The forces are identically zero for the fully enclosed cavity>> Does this mean that you agree that the force on the EM Drive's center of mass is zero? if you agree that it is zero, end of story.

If instead you meant that the forces due to the internal electromagnetic resonant (standing wave) fields are zero, but you still maintain that there is a net force on the EM Drive's center of mas due to evanescent waves on the exterior of the EM Drive, then one has to question

A) the Boundary Conditions you have on the exterior rectangular box surrounding the EM Drive and B) the dimensional extent of this rectangular box.

If the EM Drive is in outer space (ignoring a frame dependent (?) Quantum Vacuum or any other frame dependent field that you did not model, did you (?)) there is no such finite-extent box surrounding the EM Drive is there? So one would have to model a medium that extends to infinity for all practical purposes rather than a box surrounding the EM Drive which has dimensions comparable to the EM Drive.

What happens to the force on the EM Drive's center of mass if you make that box 10, or 100 times larger?

Yes, they do, or at least the forces do decay. Whether exponentially or by some other rule, they do decay.

I am suggesting that the EM thruster generates thrust force as follows:

1 - Electromagnetic energy departs the cavity via superluminal evanescent waves. See the paper that I quoted previously for justification of superluminal evanescent waves.2 - The evanescent waves remain attached to the cavity (they do not propagate) and reach a maximum distance at which point they collapse and the energy returns to the cavity, either at the point of exit or some other attachment point. I think this is reasonably well accepted by theory.3 - The evanescent waves, departing the cavity carried superluminal momentum which was reacted against the cavity. However, once the waves reach maximum distance and return to the cavity, there is no driving energy to cause them to return superluminally. Once the wave has fully collapsed, it has returned momentum p = m c, to the cavity, acting on the cavity.

It is the difference between p = m vsl reacting on the cavity, and p = m c acting on the cavity that results in a thrust force from the EM thruster.

This force is easy to calculate, it is p = m * ( vsl - c). What is harder to calculate is the value of vsl but the referenced paper gives formulas to calculate that value based on engineering parameters.

Yes, they do, or at least the forces do decay. Whether exponentially or by some other rule, they do decay.

I am suggesting that the EM thruster generates thrust force as follows:

1 - Electromagnetic energy departs the cavity via superluminal evanescent waves. See the paper that I quoted previously for justification of superluminal evanescent waves.2 - The evanescent waves remain attached to the cavity (they do not propagate) and reach a maximum distance at which point they collapse and the energy returns to the cavity, either at the point of exit or some other attachment point. I think this is reasonably well accepted by theory.3 - The evanescent waves, departing the cavity carried superluminal momentum which was reacted against the cavity. However, once the waves reach maximum distance and return to the cavity, there is no driving energy to cause them to return superluminally. Once the wave has fully collapsed, it has returned momentum p = m c, to the cavity, acting on the cavity.

It is the difference between p = m vsl reacting on the cavity, and p = m c acting on the cavity that results in a thrust force from the EM thruster.

This force is easy to calculate, it is p = m * ( vsl - c). What is harder to calculate is the value of vsl but the referenced paper gives formulas to calculate that value based on engineering parameters.

Can you please show results for force on the center of mass of the EM Drive and evanescent-wave images (showing the electromagnetic fields inside and outside the EM Drive) for the same case without the dielectric (for an empty cavity) ?

This force is easy to calculate, it is p = m * ( vsl - c). What is harder to calculate is the value of vsl but the referenced paper gives formulas to calculate that value based on engineering parameters.

Well (skipping the controversial subject of a superluminal speed vsl and the discussion in the referenced paper involving tachyons), just addressing the force, as you know p is the momentum, while the force is the rate at which momentum changes with respect to time (F = dp/dt) : therefore the average force would be given by that momentum change divided by the time interval in which that momentum change takes place.

This force is easy to calculate, it is p = m * ( vsl - c). What is harder to calculate is the value of vsl but the referenced paper gives formulas to calculate that value based on engineering parameters.

Well (skipping the controversial subject of a superluminal speed vsl and the discussion in the referenced paper involving tachyons), just addressing the force, as you know p is the momentum, while the force is the rate at which momentum changes with respect to time (F = dp/dt) : therefore the average force would be given by that momentum change divided by the time interval in which that momentum change takes place.

Yes - my bad.

We also know from our previous work that F is proportional to Q and I suspect that Q in free space for the evanescent waves could be considered to equal 1, although Q is probably not defined in that case. I'm not sure where to go with that at the moment.

Can you please show results for force on the center of mass of the EM Drive and evanescent-wave images (showing the electromagnetic fields inside and outside the EM Drive) for the same case without the dielectric (for an empty cavity) ?

I can try. The run will take several hours and may not give useful images.

As you know from our discussions of a few days (weeks) ago, Harminv does not calculate resonant frequency very accurately. (I did get independent confirmation on that point.) So my best guess will be to use the same drive frequency as before?? That is what I used for yesterday's image but that data was from Paul March and seems to be pretty solid. In that case, Harminv calculated Q = O(1000) , much lower that Paul's data, but by looking at the images each half- period, the cavity looked to be in resonance. I don't know what I'll see without the dielectric and I am assuming you'd like to see results for a vacuum filled cavity? As opposed to air filled?

I'm pursuing a work-around to determine resonance without using Harminv, but I'm not there yet.

It will be a little while before I set-up and start the run so if you have further guidance, it might be helpful.

Edit: Just a further note, the difference between air filled and vacuum filled cavity is not really detectable from looking at the field patterns.

Can you please show results for force on the center of mass of the EM Drive and evanescent-wave images (showing the electromagnetic fields inside and outside the EM Drive) for the same case without the dielectric (for an empty cavity) ?

I can try. The run will take several hours and may not give useful images.

As you know from our discussions of a few days (weeks) ago, Harminv does not calculate resonant frequency very accurately. (I did get independent confirmation on that point.) So my best guess will be to use the same drive frequency as before?? That is what I used for yesterday's image but that data was from Paul March and seems to be pretty solid. In that case, Harminv calculated Q = O(1000) , much lower that Paul's data, but by looking at the images each half- period, the cavity looked to be in resonance. I don't know what I'll see without the dielectric and I am assuming you'd like to see results for a vacuum filled cavity? As opposed to air filled?

I'm pursuing a work-around to determine resonance without using Harminv, but I'm not there yet.

It will be a little while before I set-up and start the run so if you have further guidance, it might be helpful.

Edit: Just a further note, the difference between air filled and vacuum filled cavity is not really detectable from looking at the field patterns.

Concerning

"the difference between air filled and vacuum filled cavity is not really detectable from looking at the field patterns",

this is to be expected since all that MEEP knows about the difference between air and vacuum are the values of electric permittivity and magnetic permeability, which are very close for air and vauum.

Therefore it does not really make much difference whether you would like to run it with air or vacuum. To make your job simpler for comparison, I would say run it with the same medium (air or vacuum) you had in the previous comparison you showed for the evanescent waves.

Concerning excitation frequency, we are interested in two frequencies:

A) a run with an excitation frequency of 2168 MHz to compare with NASA's experiment at that frequency without the dielectric.

B) We are also interested in a run with the same excitation frequency you already used for previous comparison you showed for the evanescent waves.

Since B) may be easier, more expedient, for you to run first (all you have to do is to set the dielectric property: electric permittivity equal to the one you used for the empty section of the cavity) you might as well run case "B" first and run "A" after that.

That is what I used for yesterday's image but that data was from Paul March and seems to be pretty solid. In that case, Harminv calculated Q = O(1000) , much lower that Paul's data, but by looking at the images each half- period, the cavity looked to be in resonance.

?

And your question is what is the relevance of this Harminv calculated Q = O(1000) ?

That is what I used for yesterday's image but that data was from Paul March and seems to be pretty solid. In that case, Harminv calculated Q = O(1000) , much lower that Paul's data, but by looking at the images each half- period, the cavity looked to be in resonance.

?

Here is an attempt to answer:

Aero may be expressing concern as to whether his MEEP modeling is showing the same resonant frequency and mode shapes modeled by COMSOL at NASA Eagleworks.

I don't recall seeing an identical replication by aero with MEEP of the mode shape and frequency of resonance modeled by COMSOL of the tests at NASA Eagleworks.

The comparison I recall for the NASA tests done in air showed aero's MEEP modeling (the posted movie) to be at a significantly lower frequency and what is even more important a very different TE mode shape, having 3 half-waves in the longitudinal direction of the cone. This is different from the latest COMSOL modeling showing (barely) 2 half-waves in the longitudinal direction for TM212, and different from the prior COMSOL modeling showing 2 half-waves in the longitudinal direction for TE012 .

The big difference is that COMSOL shows attenuation in the longitudinal direction , with a low intensity field in the dielectric for a TM212 mode, while aero's MEEP run did not show such attenuation for a TE mode. And the mode shape shown by MEEP was not the TE012 mode shape modeled by COMSOL (in the Brady report) either, because the MEEP analysis showed half-waves in the circumferential direction, while TE012 should have a constant electric field in the circumferential direction. Given these large differences between aero's MEEP and COMSOL's resonance ( differences in mode shape and frequency) it is probably unwarranted for me to say anything about the Q shown by aeros' present MEEP analysis.

My recollection is that aero in the past showed some runs with extremely high values of Q at resonance. So if aero got a Q=1000 it may mean that this latest run is signficantly away from the resonant peak (everything else being the same).

Actually, my concern is that the resonance frequency calculated by Harminv is as much as 3% off the peak. I don't know how that is related to the Q value it calculates but I worry that Harminv is sampling amplitude at that frequency to compute Q, and for a very sharp resonance peak, 3% off the peak would be way down on the shoulder. So the Q value might be meaningless.

As I wrote above, I am pursuing a work-around but I can't do meep runs and also load new software at the same time, let alone test the results against meep. i'm currently limping along with suspect software. Fortunately, Harminv is an independent module so it is not a part of the meep runs showing the field images. It does not run unless invoked by the control file.

Yes, I have shown some very high Q values as might be expected from a lossless (perfect metal) cavity. That was before I suspected a problem. Now the question arises, "Was that Q value actually for the resonance frequency calculated or was it for an adjacent resonance frequency which failed the minimum Q test, (Q > 50). Or even one that didn't fail, but was just not very interesting relatively?

The empty cavity is running now, hopefully we'll have some field images soon.

Actually, my concern is that the resonance frequency calculated by Harminv is as much as 3% off the peak.

I'm not clear about the meaning of this. Please clarify:

How do you know that the resonance frequency calculated by Harminv is as much as 3% off the peak? What peak are you referring to? Are you calculating a peak by other means than Harminv? Are you referring to the frequency reported by NASA?

I mentioned earlier that I had obtained independent confirmation of the Harminv discrepancy. Dr. Filip Dominic made some runs sampling the cylindrical resonator fields from meep, then analysed them using software independent of the meep package. He worked on it for about a week and determined that the Harminv values were off. They come closer as resolution is increased but my computer won't run this model at the high resolution needed to get closer.

Dr. Dominic sent me the software that he developed to do the analysis and that is part of my work around so I hope to have confidence in the resonance frequency. The only real problem I have is that his software is in Python, a language that I will need to practice with before I can have any certainty.

I mentioned earlier that I had obtained independent confirmation of the Harminv discrepancy. Dr. Filip Dominic made some runs sampling the cylindrical resonator fields from meep, then analysed them using software independent of the meep package. He worked on it for about a week and determined that the Harminv values were off. They come closer as resolution is increased but my computer won't run this model at the high resolution needed to get closer.

Dr. Dominic sent me the software that he developed to do the analysis and that is part of my work around so I hope to have confidence in the resonance frequency. The only real problem I have is that his software is in Python, a language that I will need to practice with before I can have any certainty.

Guys.I'm reluctant to say this, but maybe some of the previous posts would be better of as PM's to each other?I follow this thread avidly and I don't want to see it shut down again.Maybe have a think?

1) As explained here http://forum.nasaspaceflight.com/index.php?topic=29276.msg1301657#msg1301657, the previous long thread (which due to its extreme length would have been eventually locked to start a new thread anyway) was locked because of personal attacks and "stupid" and "pointless" posts "that did not feel like this site's subject matter." Specifically, posts (sometimes involving ad hominem attacks) not dealing with this thread's subject: (Microwave ) EM Drive developments.

2) We are pursuing an examination of the EM Drive related to space flight applications, specifically an examination of the latest test results by NASA Eagleworks. There are no personal attacks involved or stupid posts, hence I fail to see on what grounds you are concerned about present shutdown of the thread.

3) This EM Drive technology has now been repeatedly tested (experimentally ) at NASA in the USA, in the UK and in China. The latest results announced by Paul March just a few days ago show that NASA has validated the EM Drive in a vacuum, which eliminates the explanation (rampant in the media) that the EM Drive results were due to thermal convection currents in the air. The experimental results of these measurements reportedly produce thrust/PowerInput that are within practical SpaceFlight Applications. Such spaceflight applications have been discussed in several reports by NASA and in this thread. So, assuming that the experimental results at NASA, UK and China are not all artifacts, the subject being discussed here is not just a theory (unlike some threads in the "Advanced Concepts" section of the NASA SpaceFlight Forum that discuss topics that are much further away from SpaceFlight applications).

3 - The evanescent waves, departing the cavity carried superluminal momentum which was reacted against the cavity. However, once the waves reach maximum distance and return to the cavity, there is no driving energy to cause them to return superluminally. Once the wave has fully collapsed, it has returned momentum p = m c, to the cavity, acting on the cavity.

It is the difference between p = m vsl reacting on the cavity, and p = m c acting on the cavity that results in a thrust force from the EM thruster.